Only two summers ago television's Spitting Image update, Headcases, ran a withering puppet skit on Andy Murray. Starting a pop career, the mournful doll sang "The sun has got his hat on" in a grating monotone after the announcer had introduced him thus: "Andy Murray's joyless moaning is the sound of the summer!"

As recently as 2008 that kind of dour-Scot satire chimed with the superficial view of Murray's personality. His undergraduate-slouch was manna for news columnists desperate for something to say about Wimbledon that kept them clear of forehand drives. Tim Henman had taken years of scorn for being too nice, too Home Counties, and now Murray was fending off derision for being too horrible, too Scottish, too Kevin the Teenager.

These sort of judgments pour into the void when the tennis itself leaves a country short of proper conversational balls to hit back and forth across the net. The tear-inducing British exit from the grand slam tennis event exhausted itself as a breakfast-table subject long ago, so the middle classes made merry with character assassinations and rampant national stereotyping. As a Scot, Murray served up a whole new excuse to stir Anglo-Caledonian antipathies.

Clear-eyed observers of popularity ratings will notice that Murray's unpopularity has decreased in direct proportion to his success in big events. In other words the public are saying: he may be an uncommunicative brooder, but he's our uncommunicative brooder, and he seems better equipped to lay Fred Perry's ghost to rest than Henman ever was, so the disparagement can stop in favour of a communion round the TV set this Sunday morning.

The inability of any British male tennis player to win a grand slam title since Perry won the US Championship in 1936 is the outstanding anomaly in sport on these islands. Anomaly is putting it nicely. Sphincter-twisting embarrassment might be a better characterisation.

Murray has always had the good sense not to dress himself up as a national redeemer, though he did sign a big deal to wear Perry's minimalistic gear. British gladiator is not a role he applied for and at Wimbledon he is careful to keep the Guildford tendency at bay.

In Melbourne, before Roger Federer joined him in the final, Murray offered further evidence of his priorities: "I want to win it for the people I work with, for my parents, who helped me when I was growing up. Then, doing it for British tennis and British sport would be excellent as well."

This disinclination to accept the post assigned to him by adherents of Henmania, Andymonium and other summer cults of thwarted optimism cost him popularity points. A curiosity of tennis is that it's a sport for lone hunters who come under national banners only occasionally for the Davis Cup. But they have to pretend they go on court with a flag wrapped round their brain. Murray never made this concession. Which young British men's tennis player with an IQ above 11 would want to drape himself in the union flag – the ensign of doom?

Success – or its apparent imminence – prompts the audience to overlook the parts of the Murray package that grate on them. It will not matter today that a Wimbledon punter once called him "Gordon Brown's lovechild", or that Max Clifford reckoned he could make £100m if he "changed his attitude", but only half that sum if he kept the smacked-arse face. Nor will it count that Pat Cash once dismissed him in these pejorative terms: "Murray is never going to be eye candy and he has the most boring, monotone voice in the history of the planet."

A voice that says little and eschews stupidity is preferred by most of us to the one that says a lot stupidly. A regrettable outcome of Murray's uneasy dance with his public is that he is now gaffe-paranoid and so even less interesting in his public pronouncements. Only by being sick in the chairman of the All England Club's strawberries could he have fallen flatter than his joke about supporting "whoever England are playing" at a World Cup. Saying he and his opponent had "played like women" in the first set of a match also brought the kind of reaction that persuades a young athlete to keep his mouth zipped from now on.

Satire has largely disappeared from the coverage of his exploits. The crowd see his lifeguard physique and feel the seriousness of his quest. They watch him fighting through to the end of matches instead of wilting half-way through. They have seen the baseball cap coming off and the loose slacker's tops go in the bin. All these tiny deportment details add up in the minds of people who don't know much about tennis but like to see an authentic talent fulfilling its potential.

The other day, a movie-going web jockey compared him to Napoleon Dynamite, and there is, indeed, a resemblance. But the off-stage jabbering no longer defines Murray's life. Fickleness dictates that the changes he made to his image and his arrival in two grand slam finals (the 2008 US Open, and now) were sufficient to make the British public concentrate on the game and pipe down about his scowl and his voice.

He has matured and adjusted. That goal eludes the stubborn minority who judge him for things that hardly matter.